1. How do you change the root password? Having it as what is by default seems fairly insecure to me. I'd like to change it, preferably to something nice and long.

2. I've created a non-root user that I'd like to use in place of 'tux'. How do I make this new account the default user that logs in when the system starts? And how can I make sure that they have all the correct permissions etc. From my experience with permissions in the past, the default user is often given custom permissions, somewhere between user and admin.

i. as root edit /etc/slim.conf
ii. change 'default user' to the user name you have created.
iii. with regards to having permissions, you can use 'addgroup' command to add the new user name to various groups you want access to. /etc/group file will show you which groups tux belongs to - so adding your new user to the same groups should do the trick.